F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

398 Prestressed concrete continuous beams
Tendon B Centroidal axis
Fig.lO.S-2
(c) If the general shapes of profiles A and B are as shown, then the
prestressing force in tendon B would produce an upward reaction at
the middle support.
(d) Since tendon B follows the line of pressure of tendon A, it (tendon B)
cannot produce any shear force on the beam.
SOLUTION
(a) False. In fact profile B is concordant; see Rule 3 in Section 10.3.
(b) False. The hogging bending moment at a typical section is
P(ep of B + eP of A)
That is, the eccentricity eP of the line of pressure should be used, and
not the tendon eccentricity es. However, in this case eP of A = es of
B (why?) = ep of B (why?). Therefore hogging bending moment =
2P x (ep of B). This applies everywhere, even at section X-X!
(c) False. Tendon B is concordant (why?); therefore no reaction is
induced.
(d) False. From eqn (10.4-13), the shear force due to tendon B is
( ) d(ep of B)
VP B = -P dx
Note that Vp(A) = Vp(B) so that the shear force experienced by the
beam is twice that given above.
Comments
The authors' experience is that students tend to have difficulties with the
analysis and design of prestressed concrete continuous beams. These
difficulties are due to the lack of a clear understanding of the principles of
mechanics as applied to prestressing. This chapter has been written with the
aim of helping the student develop such an understanding and Examples
10.5-2 and 10.5-3 provide a test of his mastery of the fundamental
principles.
References 3-8 provide further insight into the fundamental behaviour
of prestressed concrete beams.
Problems
10.1 The figure shows a continuous prestressed concrete beam of uniform
cross-section. The cross-sectional area is 200 x 10 3 mm 2 and the sectional